Réponse :
Explications étape par étape :
1) Un= 1/4 (2^n + 4n - 5)
Uo = 1/4 * (1 - 5) = - 4/4 = - 1
U1 = 1/4(2 + 4 - 5) = 1/4 * 1 = 1/4
Vn= 1/4 (2^n - 4n + 5)
Vo = 1/4 * ( 1 + 5) = 6/4 = 3/2 = 1,5
V1 = 1/4 (2 - 4 + 5) = 1/4 * 3 = 3/4
2) An = Un + Vn
An = 1/4 (2^n + 4n - 5) + 1/4 (2^n - 4n + 5)
= 2^n/4 + 4n/4 - 5/4 + 2^n/4 - 4n/4 + 5/4
= 2 x (2^n/4)
= (2 x 2^n)/4
= 2^(n+1)/ 2^2
= 2 ^(n + 1 - 2)
= 2^(n-1)